I have stumbled upon this site (strangely enough) while researching what options are open for learning Latin.

I am currently doing background research on a book I am compiling for an artist who draws much of his inspiration from the ideas of Da Vinci, and who works quite a lot in Latin, so I would like give myself some grounding in the language.

I'm going to start looking at these lessons straight up, but I do have a question - is there a difference between the Latin used by the Romans and that used by da Vinci and his contemporaries - shall we say the Latin used between 1450 and 1550?

It depends upon the Latin you are dealing with. If we speak of mere Latin used by humanists from XVI-XVIII centuries (not counting Italian humanists as Dante, Petrarca, Boccaccio, &c., because their Latin is -mainly orthographically different), it tries to imitate Classical style (based mainly upon Cicero). So, if you learn "standard" (i.e., Classical) Latin, you would be able to study the ca. 2400 years of Latin literature. Another thing is Ecclesiastical Latin and Botanical Latin which you could understand from a basic Latin background.

Yes, but with some caution because not all those writers are good ones and you could find that some authors use expressions taken from their own language which don't make any sense at all in Latin. Anyway, Justus Lipsius, Joseph Justus and Julius Caesar Scaliger, Pico della Mirandola, Melanchthon, Valla, Grotius, Leon Battista Alberti, Erasmus, etc., use to be understandable when you have a considerable skill in Latin. If you can read Cicero, then they will be affordable. Erasmus, for instance, is difficult sometimes because -in my opinion- he has an exaggerated style, but they all tend to imitate Cicero -which seeks for equilibrium and harmony.By the way, when someone begins to study Classics or has any interest in it, I use to recommend William Harris' personal page (this one concretely) because it's really interesting and offers a lot of information.